Understanding how people attribute behavior to underlying mental states is crucial to the study of human social interactions. Previous research has established that people rely on attributing mental states to interpret and interact with artificial agents. For example, a pedestrian encountering a driverless vehicle at a crosswalk might view the vehicle as knowing (or not) that there is a pedestrian in front of it. Nevertheless, little attention has been devoted to investigating people's attributions of higher-order mental states, i.e., mental states that are about the mental states of others (e.g., the vehicle's beliefs about the pedestrian's intentions). Addressing this research gap, the present study conducted a survey to explore people's attributions and preferences concerning higher-order mental states in three types of artificial agents (AI chatbot, virtual assistant, and self-driving car), alongside two human agents (participants themselves, referred to as you, and five-year-old child). The survey revealed that: (1) artificial agents, in contrast to humans, may be perceived as more likely to have higher-order mental states than first-order mental states, depending on the purpose or function of the agent; (2) people may prefer some artificial agents to have mental states of a particular order (but not others); (3) attributions and preferences regarding mental states in artificial agents do not always match. The study also contributes insights regarding the methodological challenge of constructing a survey that effectively captures participants' higher-order attributions while minimizing excessive cognitive demands. We posit that human-agent interaction research and design stand to benefit from further exploration of people's attributions and preferences regarding higher-order mental states in artificial agents.